Question

(b). Solve for x and verify the result: 5x + 3 = 4/3 (1+x)​

Answer 1

Solution :

${\dashrightarrow\sf{5x + 3 = \dfrac{4}{3} \bigg(1 + x \bigg)}}$

${\dashrightarrow\sf{3 \bigg(5x + 3 \bigg)= 4\bigg(1 + x \bigg)}}$

${\dashrightarrow\sf{\bigg(5x \times 3 + 3 \times 3 \bigg)= \bigg(1 \times 4 + x \times 4 \bigg)}}$

${\dashrightarrow\sf{\bigg(15x + 9 \bigg)= \bigg(4 + 4x\bigg)}}$

${\dashrightarrow\sf{15x - 4x =4 - 9 }}$

${\dashrightarrow\sf{11x =4 - 9 }}$

${\dashrightarrow\sf{11x = - 5 }}$

${\dashrightarrow\sf{x = - \dfrac{5}{11}}}$

$\bigstar{\underline{\boxed{\sf{\red{x = - \dfrac{5}{11}}}}}}$

∴ The value of x is -5/11.

$\begin{gathered}\end{gathered}$

Verification :

${\dashrightarrow\sf{5x + 3 = \dfrac{4}{3} \bigg(1 + x \bigg)}}$

${\dashrightarrow\sf{ \bigg(\left\{5 \times - \dfrac{5}{11} \right\} + 3 \bigg)= \dfrac{4}{3} \bigg(1 + \left\{ - \dfrac{5}{10}\right\}\bigg)}}$

${\dashrightarrow\sf{ \bigg(\left\{- \dfrac{25}{11} \right\} + 3 \bigg)= \dfrac{4}{3} \bigg(1 + \left\{ - \dfrac{5}{11}\right\}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{ - ( 25 )+ (3 \times 11)}{11} \bigg)= \dfrac{4}{3} \bigg( \dfrac{(1 \times 11) - (5 \times 1)}{11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{ - 25+ 33}{11} \bigg)= \dfrac{4}{3} \bigg( \dfrac{11 - 5}{11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \dfrac{4}{3} \bigg( \dfrac{6}{11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\dfrac{4}{3} \times \dfrac{6}{11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\dfrac{4 \times 6}{3 \times 11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\dfrac{24}{33}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\cancel{\dfrac{24}{33}}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg({\dfrac{8}{11}}\bigg)}}$

$\bigstar{\underline{\boxed{\sf{\red{LHS = RHS}}}}}$

∴ Hence Verified !

Answer 2

Answer:

$x = - \frac{5}{11}$

Step-by-step explanation:

$5x + 3 = \frac{4}{3} (1 + x) \\ 5x + 3 = \frac{4}{3} + \frac{4x}{3} \\ 5x - \frac{4x}{3} = \frac{4}{3} - 3 \\ \frac{3(5x) - 4x}{3} = \frac{4 - 3(3)}{3} \\ \frac{15x - 4x}{3} = \frac{4 - 9}{3} \\ \frac{11x}{3} = - \frac{5}{3} \\ 11x = - \frac{5}{3} \times 3 \\ 11x = - 5 \\ x = - \frac{5}{11}$